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Consider the integral Use the integration by parts formula to rewrite this integral as a simpler expression (i.e. an expression that contains an integral that you already know how to calculate), as outlined in the video. Then select the option below that summarizes your work. O a Let f(z)= eg (2) =z Then f'(z) = e², 9(z) = }z² and ze² dr E Let f(z) - 1,9' (z) – e. Then f'(x) = 1,9(z) =e and re dr e- dz - re OC Let f(z) = z.g(z)=e². Then f'(z) – 1, g(z) – e² and Let f(z) = e",g'(z) – z Then f'(z) = 7 g(z) =1 and Now calculate re dz by calculating the integral that appears in your answer to question 2. Select your answer from the options below. of dr- ze +C oon d. e.

Consider the integral Use the integration by parts formula to rewrite this integral as a simpler expression (i.e. an expression that contains an integral that you already know how to calculate), as outlined in the video. Then select the option below that summarizes your work. O a Let f(z)= eg (2) =z Then f'(z) = e², 9(z) = }z² and ze² dr E Let f(z) - 1,9' (z) – e. Then f'(x) = 1,9(z) =e and re dr e- dz - re OC Let f(z) = z.g(z)=e². Then f'(z) – 1, g(z) – e² and Let f(z) = e",g'(z) – z Then f'(z) = 7 g(z) =1 and Now calculate re dz by calculating the integral that appears in your answer to question 2. Select your answer from the options below. of dr- ze +C oon d. e.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 30EQ
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1) Can you calculate this integral using the substitution method? 2) consider the integral 3) calculate xe^x dx by calculating the integral that appears in your answer to question 2
Consider the integral Use the integration by parts formula to rewrite this integral as a simpler expression (Le. an expression that contains an integral that you already know how to calculate), as outlined in the video. Then select the option below that summarizes your work. O a Let f(z) =&,g (z) = z. Then f'(z) = ē , g(z) = }z² re² dr and Let f(z) = 1,9(z) – e. Then f'(z) = 1, 9(z) – č and re dr e- ler f(=)=z.9 (2) – e. Then f'(z) – 1,9(=) = e* and ze" dz = ze" - | è dz. d Let f(z) = 2,9'(z) – z Then f'(=) – e" , g(z) = 1 and ce dz - e² Now calculate re dz by calculating the integral that appears in your answer to question 2. Select your answer from the options below. of dr- re +C bon Od.
Transcribed Image Text:Consider the integral Use the integration by parts formula to rewrite this integral as a simpler expression (Le. an expression that contains an integral that you already know how to calculate), as outlined in the video. Then select the option below that summarizes your work. O a Let f(z) =&,g (z) = z. Then f'(z) = ē , g(z) = }z² re² dr and Let f(z) = 1,9(z) – e. Then f'(z) = 1, 9(z) – č and re dr e- ler f(=)=z.9 (2) – e. Then f'(z) – 1,9(=) = e* and ze" dz = ze" - | è dz. d Let f(z) = 2,9'(z) – z Then f'(=) – e" , g(z) = 1 and ce dz - e² Now calculate re dz by calculating the integral that appears in your answer to question 2. Select your answer from the options below. of dr- re +C bon Od.
Recall. We've already seen that the method of u-substitution can help us integrate some products of functions, e.g. to calculate the integral we can make the substitution u = 1, du = 2z dz to get z sin(z²) dz = Suppose we were instead asked to calculate the integral z sin(z) dz. Can you calculate this integral using the method of substitution? O a. No! Substitution does not help us in this case. Ob. Yes, substituting u-z allows us to calculate the integral! Yes, substitution u = z sin(z) allows us to calculate the integral! Od. Yes, substituting u- sin(z) allows us to calculate the integral!
Transcribed Image Text:Recall. We've already seen that the method of u-substitution can help us integrate some products of functions, e.g. to calculate the integral we can make the substitution u = 1, du = 2z dz to get z sin(z²) dz = Suppose we were instead asked to calculate the integral z sin(z) dz. Can you calculate this integral using the method of substitution? O a. No! Substitution does not help us in this case. Ob. Yes, substituting u-z allows us to calculate the integral! Yes, substitution u = z sin(z) allows us to calculate the integral! Od. Yes, substituting u- sin(z) allows us to calculate the integral!
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